Man with inside information close to government (4)
I believe the answer is:
gent
'man' is the definition.
(gent is a kind of man)
'with inside information close to government' is the wordplay.
'with' is a charade indicator (letters next to each other).
'inside information' becomes 'gen'.
'close to' suggests the final letters (the close/ending of).
The final letter of 'government' is 't'.
'gen' put next to 't' is 'GENT'.
(Other definitions for gent that I've seen before include "Auctioneer's tool" , "Informal and short man" , "cove" , "bloke" , "Chap, fellow" .)